The formula to calculate the Moment of Inertia (I) is:
\[ I = \frac{M \cdot r^2}{2} \]
Where:
The Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
The Mass of the Body is the quantity of matter in a body regardless of its volume or of any forces acting on it.
The Radius of the Body is a radial line from the focus to any point of a curve.
Let's assume the following values:
Using the formula:
\[ I = \frac{M \cdot r^2}{2} \]
Evaluating:
\[ I = \frac{12.6 \cdot 2.1^2}{2} \]
The Moment of Inertia is 27.783 kg·m².
| Mass of Body (kg) | Radius of Body (m) | Moment of Inertia (kg·m²) |
|---|---|---|
| 10 | 1 | 5.0000 |
| 10 | 1.5 | 11.2500 |
| 10 | 2 | 20.0000 |
| 10 | 2.5 | 31.2500 |
| 10 | 3 | 45.0000 |
| 12 | 1 | 6.0000 |
| 12 | 1.5 | 13.5000 |
| 12 | 2 | 24.0000 |
| 12 | 2.5 | 37.5000 |
| 12 | 3 | 54.0000 |
| 14 | 1 | 7.0000 |
| 14 | 1.5 | 15.7500 |
| 14 | 2 | 28.0000 |
| 14 | 2.5 | 43.7500 |
| 14 | 3 | 63.0000 |
| 16 | 1 | 8.0000 |
| 16 | 1.5 | 18.0000 |
| 16 | 2 | 32.0000 |
| 16 | 2.5 | 50.0000 |
| 16 | 3 | 72.0000 |
| 18 | 1 | 9.0000 |
| 18 | 1.5 | 20.2500 |
| 18 | 2 | 36.0000 |
| 18 | 2.5 | 56.2500 |
| 18 | 3 | 81.0000 |
| 20 | 1 | 10.0000 |
| 20 | 1.5 | 22.5000 |
| 20 | 2 | 40.0000 |
| 20 | 2.5 | 62.5000 |
| 20 | 3 | 90.0000 |